1. See the recipe for Basic Pie Crust or use your own crust recipe. Keep pie crust refrigerated until ready to use.
2. Place a pizza stone in the center of the grill. Place a baking rack on the stone. Turn the burners directly below the pizza stone to low and allow the grill to slowly heat up. Adjust the heat as needed to reach a temperature of 350º.
3. Gently toss together the apples and lemon juice in a large mixing bowl. Add sugar, cornstarch, brown sugar, cinnamon, and nutmeg. Gently toss again.
4. Whisk together egg white and water. To prevent sogginess, brush the bottom and sides of the pie crust before adding the filling.
5. Roll out the dough (from the pie crust recipe) into a circle about 1/8 of an inch thick. Lay the dough across the top of the apples. Pinch off excess dough. Brush the top with egg wash and cut a few slits into the top of the pie to allow steam to escape.
6. Bake the pie for about 50 minutes on the rack and the last 10 minutes on the pizza stone, or until apples are soft. Allow to cool before serving. This recipe makes enough filling for two standard pies or one very large pie.